Lets assume I have a set of basis functions $h_1(x),h_2(x), ...$ spanning the whole hilbert space of one dimensional square integrable functions. Now I want a basis set that spans the the whole hilbert space of two dimensional square integrable functions $f_1(x,y),f_2(x,y),...$. Is it correct that all possible combinations of products $h_m(x)h_n(y)$ form such a basis? How would one prove that? Thanks very much ...
2026-04-03 10:53:44.1775213624
product of one dimensional basis functions spanning two dimensional space
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